Question

a. indicate whether the function describes exponential growth or decay. b. give the constant percentage change. $$ f(x)=72\left(1.05^{x}\right) $$

Name: Problem 5, Chapter 1: Calculus Concepts
Uploaded: 2021-10-04T23:46:14-08:00
Duration: 1 min 25 s
Channel: Kian Manafi
Description: a. indicate whether the function describes exponential growth or decay. b. give the constant percentage change. f(x)=72(1.05^x)

   a. indicate whether the function describes exponential growth or decay.
b. give the constant percentage change.
$$
f(x)=72\left(1.05^{x}\right)
$$

Calculus Concepts

Donald R. LaTorre,… 5th Edition

Chapter 1, Problem 5

Instant Answer

Solved by Expert Kian Manafi

10/04/2021

Step 1

This is determined by the base of the exponent, which is 1.05 in this case. If the base is greater than 1, the function describes exponential growth. If the base is between 0 and 1, the function describes exponential decay. In our case, the base is 1.05, which is Show more…

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a. indicate whether the function describes exponential growth or decay. b. give the constant percentage change. $$ f(x)=72\left(1.05^{x}\right) $$

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Key Concepts

Constant Percentage Change

The constant percentage change in an exponential function refers to the fixed rate at which the function increases or decreases per unit increment of x. When the function is expressed in the form f(x) = a * (1+p)^x, the value p (multiplied by 100) represents the percentage change per step, indicating consistent growth when p is positive or decay when p is negative.

Exponential Functions

Exponential functions are mathematical expressions of the form f(x) = a * b^x, where 'a' is the initial value and 'b' is the base, or common ratio. These functions model processes where the rate of change is proportional to the current amount, leading to rapid growth or decay.

Exponential Growth

Exponential growth occurs when the base 'b' of the exponential function is greater than 1. In such cases, as x increases, the function's output increases at a progressively faster rate, illustrating the compounding effect of constant percentage increases.

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